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上小学 · 2023年03月26日

标准误是样本均值的标准差，是需要处以样本数量根号的，而且第一题也是求标准误。二题所用公式不一致，迷惑。谢谢

  1. FRM I
  2. Quantitative

NO.PZ2019040801000025

问题如下：

Assuming the height of a tree in a forest follows a normal distribution, there are more than 10,000 trees. The sample size of test is 200, the 95% confidence interval of the sample mean of the height is 11 to 35 meters based on a z-statistic, the standard error of mean height is closest to:

选项：

A.

1.96.

B.

3.58.

C.

6.12.

D.

10.50.

解释：

C is correct.

考点：The central limit theorem (CLT)

解析：95%的置信区间是11到 35，z值是1.96.

平均数为0.5*（11+35）=23.所以置信区间是23 ± 1.96sx, sx是标准误。23+1.96sx等于35，sx等于6.12米

第一题和第二题是一样的求标准误，没有不同。

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已采纳答案

pzqa27 · 2023年03月27日

嗨，爱思考的PZer你好：


给的条件是不一样的，这个题给的是置信区间，让我们求标准误，因此用的是下图的公式进行倒解

而第一个题给的是标准差和样本容量，直接用标准误定义式计算即可

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